Ta có :
\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...+\frac{1}{1024}\)
\(A=\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\)
\(2A=1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\)
\(2A-A=\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^9}\right)-\left(\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{10}}\right)\)
\(A=1-\frac{1}{2^{10}}\)
\(A=\frac{2^{10}-1}{2^{10}}\)
\(A=\frac{1024-1}{1024}\)
\(A=\frac{1023}{1024}\)
Vậy \(A=\frac{1023}{1024}\)
Chúc bạn học tốt ~
Đặt tổng trên là A.
Ta có
A x 2 = 1+ 1/2+1/4+1/8+ 1/16+1/32+ 1/64+ 1/128 + 1/256 + 1/512
Ax2 - A = 1+ 1/2+1/4+1/8 +1/16 + 1/32 +1/64+ 1/128 + 1/256+ 1/512 - ( 1/2 + 1/4 +1/8+1/16+1/32+1/64 + 1/128+ 1/256 + 1/512+ 1/1024)
A = 1+ 1/2 +1/4+1/8+1/16+1/32+1/64+1/128+1/256 + 1/512 - 1/2-1/4-1/8-1/16-1/32-1/64-1/128-1/256-1/512- 1/1024
A = 1 - 1/ 1024 = 1023/1024
A=1/2 + 1/4 + 1/8 + ... + 1/512 + 1/1024 (1)
Nhân cả 2 vế với 2 ta có :
A x 2 = 2 x ( 1/2 + 1/4 + 1/8 + ... + 1/512 + 1/1024 )
A x 2 = 1 + 1/2 + 1/4 + ... + 1/256 + 1/512 (2)
Lấy (2) - (1) ta có :
A x 2 - A = ( 1 + 1/2 + 1/4 + ... + 1/256 + 1/512 ) - ( 1/2 + 1/4 + 1/8 + ... + 1/512 + 1/1024 )
A x 2 - A = 1 + 1/2 + 1/4 + ... + 1/256 + 1/512 - 1/2 - 1/4 - 1/8 - ... - 1/512 - 1/1024
A = 1 - 1/1024
A = 1023/1024
\(A=\frac{1023}{1024}\)
ai trên 15 điểm thì tk mk nha
A = 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512 + 1/1024
A x 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/512
A x 2 - A = 1 + 1/2 - 1/2+ 1/4 -1/4 + 1/8 -1/8 + 1/16 -1/16 + ... + 1/512 - 1/512 - 1/1024
A = 1 - 1/1024
A = 1023/1024
